Question: The sum of two numbers is $80$, and their difference is $20$. What are the two numbers?
Solution: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 80}$ ${x-y = 20}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 100 $ $ x = \dfrac{100}{2} $ ${x = 50}$ Now that you know ${x = 50}$ , plug it back into $ {x+y = 80}$ to find $y$ ${(50)}{ + y = 80}$ ${y = 30}$ You can also plug ${x = 50}$ into $ {x-y = 20}$ and get the same answer for $y$ ${(50)}{ - y = 20}$ ${y = 30}$ Therefore, the larger number is $50$, and the smaller number is $30$.